NSW Y11 Maths - Extension 1 Functions Reciprocal Functions

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Reciprocal Functions - Video - Graphing Reciprocals of Quadratic Functions

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Given the graph \(y = f(x)\) the graph of \(y = \dfrac{1}{{f(x)}}\) is the reciprocal function.

When drawing the reciprocal function by letting \(f(x) = 0\) this will determine the vertical asymptotes of the reciprocal function.

Also, when \(f(x) \to \pm \infty \), \(\dfrac{1}{{f(x)}} \to 0\).

NSW Syllabus Reference: ME-F1.1: Graphical relationships. This will require student to

examine the relationship between the graph of \(y=f(x)\) and the graph of \(y=\dfrac{1}{f(x)}\) and hence sketch the graphs (ACMSM099)
examine the relationship between the graph of \(y=f(x)\) and the graphs of \(y^2=f(x)\) and \(y=\sqrt{f(x)}\) and hence sketch the graphs
examine the relationship between the graph of \(y=f(x)\) and the graphs of \(y=|f(x)|\) and \(y=f(x)+g(x)\) and hence sketch the graphs (ACMSM099)
examine the relationship between the graphs of \(y=f(x)\) and \(y=g(x)\) and the graphs of \(y=f(x)+g(x)\) and \(y=f(x)g(x)\) and hence sketch the graphs
apply knowledge of graphical relationships to solve problems in practical and abstract contexts